The point is, nobody really gives a damn about Earth itself, and why should we? It's a rock.

What we care about is us, humans. When we say "save the planet", what we mean is "save the ecosystem that's letting us live here, and enjoy that life". If we break things and die as a result, sure, something else will live. But we don't care about that something else, we care about us.

It's a stupid shorthand, but for some reason people appreciate the fake humility of saying it's about Earth, not about us.